Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D23 |
| Fitting | C16×C23 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D23 |
| commutator, hypocenter | C23 | C2×C16 |
| Frattini | C8 | C2×D23 |
| Fitting | C16×C23 | C2 |
| socle | C2×C23 | C2×C8 |
| prime radical | C2×D23 | C8 |
| cosocle | C8×C23 | C22 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C16 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D23, #13092250, C2×C16×D23, … |
| maximal normal subgroup of | C32×D23, #13092250, C2×C16×D23, … |
| maximal quotient of | C16×Dic23, (C2×D23)⋊C16, Dic23⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 3);